page_title: Biham–Middleton–Levine traffic model
section_title: Phase transitions
hierarchical_section_title: Biham–Middleton–Levine traffic model / Phase transitions
caption_attribution_description: English: A graph of mobility for the w:Biham-Middleton-Levine traffic model corresponding to the lattice in File:Bml x 512 y 512 p 29 iterated 0.png and File:Bml x 512 y 512 p 29 iterated 32000.png. The vertical axis represents the number of cars that can move, and the horizontal axis represents the turn. The vertical axis is normalized so tha the top edge is one and the bottom edge is zero; likewise the horizontal axis has a range of 0 to 32000. This was created with C++. Source code is located at w:user:Purpy Pupple/BML.
context_page_description: The Biham–Middleton–Levine traffic model is a self-organizing cellular automaton traffic flow model. It consists of a number of cars represented by points on a lattice with a random starting position, where each car may be one of two types: those that only move downwards, and those that only move towards the right. The two types of cars take turns to move. During each turn, all the cars for the corresponding type advance by one step if they are not blocked by another car. It may be considered the two-dimensional analogue of the simpler Rule 184 model. It is possibly the simplest system exhibiting phase transitions and self-organization.
context_section_description: Despite the simplicity of the model, it has two highly distinguishable phases – the jammed phase, and the free-flowing phase. For low numbers of cars, the system will usually organize itself to achieve a smooth flow of traffic. In contrast, if there is a high number of cars, the system will become jammed to the extent that no single car will move. Typically, in a square lattice, the transition density is when there are around 32% as many cars as there are possible spaces in the lattice.
caption: Mobility with respect to time for above lattice. Mobility is defined as the number of cars that can move as a fraction of the total. (The points are in the upper-left corner of the image.)
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